Type

There are following death animation types:

• regular
• "flying" 
• burning
• freezing
• disintegrating

Regular

Regular death animation also known as "delayed" death animation due to the fact that after wounds have been allocated to models they start to die gradually during 7-17 seconds period. 

This video explains how "delayed" death animation was discovered 

This video demonstrates delayed death animation.
1st round: goblins kill 11 humans during ~8 seconds: 2, 3, 2, 4 models die every ~2 seconds.
2nd round: goblins kill 5 humans during ~5 seconds: 2 models, after 5 seconds 3 models more
3rd round: goblins kill 4 remaining humans during ~ seconds: 1 model, after 7 seconds 2 models more, after 10 seconds last 1 model

Flying

So called flying death animation happens when unit has +2 or more strength advantage over enemy unit strength, due to unit's higher Str characteristic/weapon (i.e. great sword +2 str) or temporary bonuses (i.e. charge, potion, button boost or magic spell).
Condition for such death animation is: if unit str >= then enemy unit str then play flying death animation, else play regular death animation

Flying death animation also happens when models get hit by shell of war machine (cannon, catapult, etc.)

It is important to mention that flying death animation plays instantly as soon as wounds are allocated to models.

This video demonstrates flying death animation 

Burning

Burning death animation plays when model death caused by fire source such as magic spell, screaming catapult shell, etc.

Freezing

When creature dies from Frost magic it first gets frozen and after seconds breaks into million of shards

Disintegrating

Death magic can disintegrate target into dust